Holomorphic forms on threefolds

Name: Work Video:
Duration: 3 min 30 s
Description: Two conjectures relating the Kodaira dimension of a smooth projective variety and existence of number of nowhere vanishing 1-forms on the variety are proposed and verified in dimension 3.
Tie Luo; Qi Zhang
{'id': 'https://openalex.org/W4394656780', 'doi': 'https://doi.org/10.48550/arxiv.math/0304022', 'title': 'Holomorphic forms on threefolds', 'display_name': 'Holomorphic forms on threefolds', 'publication_year': 2003, 'publication_date': '2003-01-01', 'ids': {'openalex': 'https://openalex.org/W4394656780', 'doi': 'https://doi.org/10.48550/arxiv.math/0304022'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/math/0304022', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': 'other-oa', 'license_id': 'https://openalex.org/licenses/other-oa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'type': 'preprint', 'type_crossref': 'posted-content', 'indexed_in': ['datacite'], 'open_access': {'is_oa': True, 'oa_status': 'green', 'oa_url': 'https://arxiv.org/abs/math/0304022', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5023613713', 'display_name': 'Tie Luo', 'orcid': None}, 'institutions': [], 'countries': [], 'is_corresponding': False, 'raw_author_name': 'Tie Luo', 'raw_affiliation_strings': [], 'affiliations': []}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5100360255', 'display_name': 'Qi Zhang', 'orcid': 'https://orcid.org/0000-0002-0843-815X'}, 'institutions': [], 'countries': [], 'is_corresponding': False, 'raw_author_name': 'Qi Zhang', 'raw_affiliation_strings': [], 'affiliations': []}], 'institution_assertions': [], 'countries_distinct_count': 0, 'institutions_distinct_count': 0, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': None, 'has_fulltext': False, 'cited_by_count': 0, 'citation_normalized_percentile': {'value': 0.0, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 0, 'max': 59}, 'biblio': {'volume': None, 'issue': None, 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10061', 'display_name': 'Algebraic Geometry and Number Theory', 'score': 0.9999, 'subfield': {'id': 'https://openalex.org/subfields/2608', 'display_name': 'Geometry and Topology'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T10061', 'display_name': 'Algebraic Geometry and Number Theory', 'score': 0.9999, 'subfield': {'id': 'https://openalex.org/subfields/2608', 'display_name': 'Geometry and Topology'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T12812', 'display_name': 'Meromorphic and Entire Functions', 'score': 0.9993, 'subfield': {'id': 'https://openalex.org/subfields/2604', 'display_name': 'Applied Mathematics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T11166', 'display_name': 'Analytic Number Theory Research', 'score': 0.9975, 'subfield': {'id': 'https://openalex.org/subfields/2602', 'display_name': 'Algebra and Number Theory'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/kodaira-dimension', 'display_name': 'Kodaira dimension', 'score': 0.89577353}, {'id': 'https://openalex.org/keywords/projective-variety', 'display_name': 'Projective variety', 'score': 0.79595613}, {'id': 'https://openalex.org/keywords/complex-dimension', 'display_name': 'Complex dimension', 'score': 0.4425125}], 'concepts': [{'id': 'https://openalex.org/C2777969054', 'wikidata': 'https://www.wikidata.org/wiki/Q6425087', 'display_name': 'Kodaira dimension', 'level': 2, 'score': 0.89577353}, {'id': 'https://openalex.org/C204575570', 'wikidata': 'https://www.wikidata.org/wiki/Q207476', 'display_name': 'Holomorphic function', 'level': 2, 'score': 0.84283173}, {'id': 'https://openalex.org/C136197465', 'wikidata': 'https://www.wikidata.org/wiki/Q1729295', 'display_name': 'Variety (cybernetics)', 'level': 2, 'score': 0.8057076}, {'id': 'https://openalex.org/C62139920', 'wikidata': 'https://www.wikidata.org/wiki/Q3554818', 'display_name': 'Projective variety', 'level': 2, 'score': 0.79595613}, {'id': 'https://openalex.org/C33676613', 'wikidata': 'https://www.wikidata.org/wiki/Q13415176', 'display_name': 'Dimension (graph theory)', 'level': 2, 'score': 0.78361106}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.73211604}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.65082514}, {'id': 'https://openalex.org/C168185519', 'wikidata': 'https://www.wikidata.org/wiki/Q5156577', 'display_name': 'Complex dimension', 'level': 2, 'score': 0.4425125}, {'id': 'https://openalex.org/C177846678', 'wikidata': 'https://www.wikidata.org/wiki/Q1501864', 'display_name': 'Projective test', 'level': 2, 'score': 0.4177541}, {'id': 'https://openalex.org/C136119220', 'wikidata': 'https://www.wikidata.org/wiki/Q1000660', 'display_name': 'Algebra over a field', 'level': 2, 'score': 0.38448074}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.344412}, {'id': 'https://openalex.org/C105795698', 'wikidata': 'https://www.wikidata.org/wiki/Q12483', 'display_name': 'Statistics', 'level': 1, 'score': 0.062047303}], 'mesh': [], 'locations_count': 2, 'locations': [{'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/math/0304022', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': 'other-oa', 'license_id': 'https://openalex.org/licenses/other-oa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': False, 'landing_page_url': 'https://api.datacite.org/dois/10.48550/arxiv.math/0304022', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4393179698', 'display_name': 'DataCite API', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I4210145204', 'host_organization_name': 'DataCite', 'host_organization_lineage': ['https://openalex.org/I4210145204'], 'host_organization_lineage_names': ['DataCite'], 'type': 'metadata'}, 'license': None, 'license_id': None, 'version': None}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/math/0304022', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': 'other-oa', 'license_id': 'https://openalex.org/licenses/other-oa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'sustainable_development_goals': [{'id': 'https://metadata.un.org/sdg/10', 'score': 0.4, 'display_name': 'Reduced inequalities'}], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 0, 'referenced_works': [], 'related_works': ['https://openalex.org/W4394656780', 'https://openalex.org/W4366485329', 'https://openalex.org/W4309208295', 'https://openalex.org/W4299412404', 'https://openalex.org/W2952811895', 'https://openalex.org/W2084214200', 'https://openalex.org/W2052825011', 'https://openalex.org/W2046582509', 'https://openalex.org/W1984417042', 'https://openalex.org/W1666753794'], 'abstract_inverted_index': {'Two': [0], 'conjectures': [1], 'relating': [2], 'the': [3, 20], 'Kodaira': [4], 'dimension': [5, 27], 'of': [6, 13, 15], 'a': [7], 'smooth': [8], 'projective': [9], 'variety': [10, 21], 'and': [11, 24], 'existence': [12], 'number': [14], 'nowhere': [16], 'vanishing': [17], '1-forms': [18], 'on': [19], 'are': [22], 'proposed': [23], 'verified': [25], 'in': [26], '3.': [28]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W4394656780', 'counts_by_year': [], 'updated_date': '2024-12-13T03:28:18.176207', 'created_date': '2024-04-11'}
Publication Information

Basic Information

Access and Citation

AI Researcher Chatbot

Primary Location

Authors

Topics

Keywords

Related Works
